Massey products in the homology of the loopspace of a p-completed classifying space: finite groups with cyclic Sylow p-subgroups

TL;DR

This paper investigates the algebraic structures of the homology of loop spaces of classifying spaces for finite groups with cyclic Sylow p-subgroups, providing explicit descriptions of their A-infinity algebra structures.

Contribution

It determines the A-infinity algebra structures of the homology of the loop space of the p-completed classifying space for such groups, up to quasi-isomorphism.

Findings

H^*(BG;k) has a specific A-infinity algebra structure.

H_*(\Omega BG ext{ extasciitilde};k) has a determined A-infinity algebra structure.

The structures are explicitly described up to quasi-isomorphism.

Abstract

Let G be a finite group with cyclic Sylow p-subgroup, and let k be a field of characteristic p. Then H^*(BG;k) and H_*(\Omega BG\phat;k) are A_{\infty} algebras whose structure we determine up to quasi-isomorphism.